A Zienkiewicz-type finite element applied to fourth-order problems |
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Authors: | A.B. Andreev M.R. Racheva |
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Affiliation: | a Department of Informatics, Technical University of Gabrovo, Gabrovo and IPP-BAS, Sofia, Bulgariab Department of Mathematics, Technical University of Gabrovo, Gabrovo, Bulgaria |
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Abstract: | This paper deals with convergence analysis and applications of a Zienkiewicz-type (Z-type) triangular element, applied to fourth-order partial differential equations. For the biharmonic problem we prove the order of convergence by comparison to a suitable modified Hermite triangular finite element. This method is more natural and it could be applied to the corresponding fourth-order eigenvalue problem. We also propose a simple postprocessing method which improves the order of convergence of finite element eigenpairs. Thus, an a posteriori analysis is presented by means of different triangular elements. Some computational aspects are discussed and numerical examples are given. |
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Keywords: | 65N25 65N30 |
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